Unformatted text preview: 1 Solutions 4. A fundamental set is 107 . The matrix equation
implies and . Thus ,
, and
. Observe though
that
is a homogeneous solution and so the general solution can
be written
. The incomplete partial fraction
which implies that
method gives
is a particular solution. The general solution is as above.
5. A fundamental set is . The matrix equation
implies . Hence and ,
, and
. The
general solution is
. The method of undetermined
coeﬃcients implies that a particular solution is of the form
.
Substitution gives
and hence
. The general solution is
as above.
and 6. form a fundamental set for the homogeneous solutions. Let
. Then the matrix equation
implies that . From this we get
. Therefore and
. The general solution is
. thus
7. A fundamental set is and . The matrix equation
implies and . Hence, ,
, and
. Since
homogeneous solution we can write the general solution as
.
8. A fundamental set is . The matrix equation
implies Hence
general solution is is a , and . , and . The
. 9. The associated homogeneous equation is CauchyEuler with indicial equation
. It follows that
forms a fundamental
set. We put the given equation is standard form to get
.
Thus
. The matrix equation
implies and . Hence ...
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 Fall '08
 BELL,D
 general solution, matrix equation

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